This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modif...This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modifications(PMs)are considered.For the prediction,a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented.Then,the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion.The prediction method is validated by comparison with the experimental results from the literature,and a set of cases are simulated to study the effects of MEs,AEs,TDs and PMs on the static transmission error.In addition,the time-varying backlash caused by both MEs and AEs,and the contact ratio under load conditions are also investigated.The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades.The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.展开更多
Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification...Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.展开更多
This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled...This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.展开更多
A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time...A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.展开更多
基金Project(51675061)supported by the National Natural Science Foundation of China。
文摘This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modifications(PMs)are considered.For the prediction,a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented.Then,the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion.The prediction method is validated by comparison with the experimental results from the literature,and a set of cases are simulated to study the effects of MEs,AEs,TDs and PMs on the static transmission error.In addition,the time-varying backlash caused by both MEs and AEs,and the contact ratio under load conditions are also investigated.The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades.The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.
基金Sponsored by the National Natural Science Foundation of China(Grant No.2009AA04Z404)
文摘Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.
基金Funded by the National Natural Science Foundation of China(Grant No.51375013)the Anhui Provincial Natural Science Foundation(Grant No.1208085ME64)
文摘This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.
基金Project(51105194)supported by the National Natural Science Foundation of ChinaProject(20113218110017)supported by the Doctoral Program Foundation of Institutions of Higher Education of China+2 种基金Project supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions,ChinaProject(CXZZ11_0199)supported by the Funding of Jiangsu Innovation Program for Graduate Education,ChinaProjects(NZ2013303,NZ2014201)supported by the Fundamental Research Funds for the Central Universities,China
文摘A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.
